Abstract:

We initiate the study of the number of measurements required for quantum process tomography under prior information, such as a promise that the unknown channel is unitary. We introduce the notion of an interactive observable and we show that any unitary channel acting on a d-level quantum system can be uniquely identified among all other channels (unitary or otherwise) with only \(O(d^2)\) interactive observables, as opposed to the \(O(d^4)\) required for tomography of arbitrary channels. This result generalizes to the problem of identifying channels with at most q Kraus operators, and slight improvements can be obtained if we wish to identify such a channel only among unital channels or among other channels with q Kraus operators. These results are proven via explicit construction of large subspaces of Hermitian matrices with various conditions on rank, eigenvalues, and partial trace. Our constructions are built upon various forms of totally nonsingular matrices.

Authors:

• Gus Gutoski
• Nathaniel Johnston

Download:

• Official publication from Journal of Mathematical Physics
• Preprint from arXiv:1309.0840 [quant-ph]
• Local preprint [pdf]
• Slideshow presentation [pdf]

Cite as:

• G. Gutoski and N. Johnston. Process tomography for unitary quantum channels. Journal of Mathematical Physics, 55:032201, 2014.

Related publications:

• Uniqueness of quantum states compatible with given measurement results – a paper with many analogous results for the case of state tomography, rather than process tomography